### Citations

688 |
String Theory
- Polchinski
- 1998
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Citation Context ...ic would be to allow for quantum fluctuations of the line-like object in directions transverse to the line. Those considerations lead to (and in fact inspired) the formidable subject of string theory =-=[10]-=-. QCD can be made agree with the simple phenomenological model if, for some reason, the electric field diverging from a quark is collimated into a flux tube of fixed cross-sectional area. In that case... |

629 |
Gauge Fields and Strings
- Polyakov
- 1987
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Citation Context ...lattice with finite time extension unbroken ZN symmetry ⇔ confinement phase In other words, confinement can be identified as the phase in which global center symmetry is also a symmetry of the vacuum =-=[11]-=-. The Polyakov loop is a true order parameter: zero in one phase, non-zero in another, which associates the breaking of a global symmetry with the transition from one phase to another. This fact provi... |

30 |
in Recent Developments in Gauge Theory
- Witten
- 1979
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Citation Context ...ng ideas about confinement (see also the earlier comments in ref. [37]). There are two theoretical arguments for Casimir scaling: dimensional reduction [38, 39] and factorization in the large-N limit =-=[40]-=-. We begin with factorization. The trace of a Wilson loop holonomy U(C), in a representation r of SU(N) gauge theory, is the group character χr[U(C)], and this can always be expressed in terms of a su... |

23 |
Greensite and
- Debbio, Faber, et al.
- 1998
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Citation Context ...ate, so as to disorder these loops. In fact, this is just what happens, as seen in Fig. 23. Further support of this general picture, also obtained via center projection in DMC gauge, is found in ref. =-=[90]-=-. The deconfinement phase transition has also been investigated from the vortex free energy point of view by de Forcrand and von Smekal [19], Del Debbio, Di Giacomo, and Lucini [20], and by Hart et al... |

15 |
Annals Phys
- Lenz, Naus, et al.
- 1994
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Citation Context ...exp[iθ], and the “displacement” symmetry g(x) = exp[i � d · �x] (171) It is breaking of these remnant global symmetries which separates the Higgs from the Coulomb phase in abelian theories; c.f. ref. =-=[120]-=- for a discussion of this point. There is an important limitation of the dual abelian Higgs model, which is relevant to its applicability in a non-abelian gauge context: The dual-abelian Higgs model d... |

13 |
in Recent Developments in Gauge Theories, edited by G. ’t Hooft et al
- Mack
- 1980
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Citation Context ...Confinement Mechanism In this and the following sections we explore some possible explanations of the confining force, beginning with the proposal which is most closely tied to the ZN center symmetry =-=[13, 57, 58, 59, 60]-=-. There are several motivations for the center vortex mechanism. The first is the fact that the asymptotic string tension σr, extracted from Wilson loops in the r representation of color SU(N), depend... |

12 |
t Hooft, in High Energy Physics, edited by A. Zichichi, Editrice Compositori
- unknown authors
- 1976
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Citation Context ...ents �E → � B , � B → − � E , j e µ ↔ j m µ (168) Conservation of both the electric and magnetic currents implies separate electric and magnetic U(1) symmetries. It occurred independently to ’t Hooft =-=[117]-=- and Mandelstam [118], in 1976, that quark confinement in QCD might be due to some type of dual superconductivity, in which the QCD vacuum state can be regarded as a condensate of a magnetically charg... |

9 |
At the Frontier of Particle
- Rajagopal, Wilczek
- 2001
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Citation Context ... from a confining phase. The notion that confining and Higgs physics, in theories with fundamental matter fields, are separated by a symmetry breaking transition serves only as a “convenient fiction” =-=[8]-=-. The fiction is convenient because the spectrum of theories with “broken” gauge symmetry is qualitatively very different from the QCD spectrum. This qualitative difference is not captured very well b... |

6 |
Olejník, in New Developments in Quantum Field Theory, edited by P
- Debbio, Faber, et al.
- 1998
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Citation Context ...ontributions of virtual W-bosons to the effective action can no longer be ignored. 7.8 Monopoles and Vortices Let us now consider how center vortices would appear in the abelian projection (cf. refs. =-=[154, 150]-=-, and also ref. [77]). We begin with a center vortex at a fixed time, as indicated 79sschematically in Fig. 32. In the absence of gauge fixing, the vortex field strength points in arbitrary directions... |

4 |
Nonperturbative Aspects of QCD, edited by P
- Confinement
- 1997
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Citation Context ...on a thin vortex surface has been analyzed 56s(a) (b) Figure 25: Intersection points (a) and writhing points (b) which contribute to the topological charge of a P-vortex surface. From Reinhardt, ref. =-=[93]-=-. by Engelhardt and Reinhardt in refs. [91, 93, 75]. In general, topological charge arises at lattice sites at which the set of tangent vectors to the vortex surface span all four space-time direction... |

1 |
Smekal, in Confinement, Topology, and Other NonPerturbative Aspects of QCD, edited by J. Greensite and
- Forcrand, von
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Citation Context ..., y directions, is consistent with confining behavior (49) of the vortex free energy. The twist trick can also be used to insert center vortex flux through any plane, or several planes simultaneously =-=[17]-=-. The drop in vortex free energy with lattice size is naturally associated with the vortex “spreading out” to its natural thickness as lattice size increases. It is possible to insert constraints whic... |

1 |
hep-lat/0211004; hep-lat/0209060; and in Confinement, Topology, and Other Non-Perturbative Aspects of QCD, edited by
- Forcrand, Jahn
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Citation Context ... theory is non-confining, simply because it is impossible to introduce color sources of nonzero N-ality. The static potential therefore tends to a constant at large distances. Still, as noted in ref. =-=[26]-=-, the presumed universality of the continuum fixed point suggests that the SU(N) and SU(N)/ZN theories should be in some sense equivalent in the continuum. For example, one might expect a finite tempe... |

1 |
of Tsukuba prepreint UTHEP-118
- Iwasaki, Univ
- 1983
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Citation Context ... SI = c0 N − ReTr[U(P)] � �� + c1 N − ReTr[U(R)] � (107) P This class of actions has been widely discussed in the lattice literature, and includes the tadpole-improved action [63], the Iwasaki action =-=[64]-=-, and two-parameter approximations [65] to the Symanzik action [66] and the DBW2 action [67]. The thin vortex configuration, eq. (97), is easily shown to be a stable minimum of the action SI providing... |

1 |
At the Frontier of Particle Physics, vol. 3, edited by M
- Kovner, in
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Citation Context ...is dual formulation, appear as solitons of the effective action. This effective theory was originally proposed by ’t Hooft in ref. [13], and has been investigated extensively by Kovner and co-workers =-=[128]-=-. The action is motivated by ’t Hooft’s observation that the analog of the SU(N) vortex creation operator B(C), in 2+1 dimensions, is an operator V (x) defined such that V (x)|Ak, φ〉 = |A ′ k, φ ′ 〉 (... |

1 |
in Confinement, Topology, and Other Non-Perturbative Aspects of QCD, edited by
- Belavin, Chernodub, et al.
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Citation Context ...ated construction for the monopole operator which avoids this problem, and which makes use essential use of center vortices. Some numerical work, based on this construction, has been reported in ref. =-=[148]-=-. 74sforce. In the abelian projection 〈Tr [UA(C)]〉 → 1� m=−1 〈exp[2imθ(C)]〉 = 1 + � e 2iθ(C)� + � e −2iθ(C)� = 1 + 2e −2σ1Area(C) (214) The zero-charge component contributes a constant (one) to the tr... |

1 |
in Confinement, Topology, and Other Non-Perturbative Aspects of QCD, edited by
- Langfeld
(Show Context)
Citation Context ...s nonsingular in the infrared [161]. The effect of vortex removal on Landau gauge propagators, and its possible implications for confinement, has been investigated recently by Langfeld et al. in ref. =-=[162]-=-. 85s|k| 4 ∼ V coul (k) 45 40 35 30 25 20 15 10 5 0 5 10 15 20 k 2 [GeV 2 ] Figure 38: Coulomb energy ×|k| 4 in momentum space, at β = 2.5 in SU(2) lattice gauge theory. The solid line is a fit to eq.... |

1 |
JHEP 11 (2000) 030, hep-th/0008080. 96
- Greensite, Olesen
- 1981
(Show Context)
Citation Context ...nal superstring in a peculiar metric, which nonetheless describes the physics of D = 4 dimensional QCD. Both the Lüscher term and the logarithmic growth of the flux tube are natural in this framework =-=[47, 48]-=-. The catch is that the AdS/CFT correspondence for QCD is (so far) restricted to strong-coupling calculations with a short-distance cutoff, much like strongcoupling lattice gauge theory. The AdS/CFT c... |